Beam models for predicting dynamic elastic response

Further investigation of the three-parameter lumped mass model for the prediction of natural frequencies and transient response of Bernoulli-Euler clamped-clamped beams has resulted in a revised model, which is slightly superior to the original model, as it is applicable over a wider frequency range.     

Local geology and dynamic parameters of seismic waves

Summary Amplitudes and periods of seismic waves recorded both in the short-period and in the intermediate-period ranges at the seismic stations Prhonice, Praha and Kaperské Hory are influenced by the tectonic situation in the focal regions rather than by the anisotropic structures of the geologic formations underlying the stations. Large amplitude variations and differences in periods due to instrumental effects were also found.     

Comparison between seismic vulnerability models and experimental dynamic properties of existing buildings in France

Elastic fundamental frequency is a key-parameter of simplified seismic design and vulnerability assessment methods. Empirical relationships exist in codes to estimate this frequency but they miss experimental data to validate them accounting for national feature of building design and, above all, corresponding uncertainties. Even if resonance frequency extracted from ambient vibrations may be larger than the elastic frequency (at yield) generally used in earthquake engineering, ambient vibration recordings may provide a large set of data for statistical analysis of periods versus building characteristics relationships. We recorded ambient vibrations and estimated the fundamental frequency of about 60 buildings of various types (RC and masonry) in Grenoble City (France). These data complete the set existing yet, made of 26 RC-buildings of Grenoble (Farsi and Bard 2004) and 28 buildings in Nice (France) (Dunand 2005). Statistical analysis of these experimental data was performed for fundamental frequencies of RC shear wall structures and the results are compared with existing relationships. Only building height or number of stories has a statistical relevancy to estimate the resonance frequency but the variability associated to the proposed relationships is large. Moreover, we compared the elastic part of capacity curves of RC and masonry buildings used in the European Risk-UE method for vulnerability assessment with the experimental frequencies. The variability is also large and the curves may not be consistent with French existing buildings.     

An index for measuring the effects of topography on seismic ground motion intensity

An index is proposed for the quantitative evaluation of topographical effects, as may be required in seismic microzoning and structural design applications. This topographical effects index (TEI) is defined as the relative Arias intensity for a given position. As an example, the TEI is calculated for a semicircular canyon excited by an earthquake signal that consists of plane elastic SH waves and is characterized by a theoretical spectrum of accelerations. The analytical solution by Trifunac¹⁵ provides the transfer functions for this problem. The behaviour and spacial distribution of the calculated TEI values are illustrated for different incidence angles and spectral parameters. The proposed index appears useful for generating quantitative criteria which, after proper confirmation by instrumental recordings, could be considered in earthquake code provisions.     

地震波作用下的埋地燃气管道动力响应研究

埋地管道是现代城市的重要生命线工程,因其埋于地下,一旦遭遇地震,管道就有可能发生破坏,导致燃气泄露,可能引发火灾、爆炸等次生灾害,对人们的生命和财产造成严重威胁,因此,如何提高埋地燃气管道的抗震性能,是当前需要迫切解决的问题.认为在管道轴向上和横向上均与土体之间存在相对位移,结合拟静力法进行了地震波作用下埋地管道的动力...     

The effect of travelling seismic waves on the dynamic response of earth dams

A theoretical investigation of the dynamic response of earth dams to the travelling seismic waves is presented. The earth dam is simplified as a truncated two-dimensional elastic wedge. The dam body consists of an isotropical linear viscoelastic material with homogeneous elastic modulus and density. The seismic waves travel along the longitudinal direction of the earth dam. The numerical calculations show the following. (i) For the longitudinal mode of vibration, the greater the ratio (H/L) of the height to the lenght of the complete wedge, the more the natural transverse period of vibrational of the two-dimensional wedge is less than that of the one-dimensional wedge. Especially for the first two natural transverse period, this influence is large. The decrease of the ratio of the natural transverse period for a two-dimensional wedge to that for a one-dimensional wedge with the ratio H/L is rapid for the higher than for the lower longitudinal modes. (ii) Comparing with the one-dimensional wedge, the natural transverse periods for the two-dimensional case in the complete wedge are lower, and they will increase as the coefficient of truncation, h/H increases. (iii) When the frequency of forced vibration is less than the natural transverse frequency for one-dimensional wedge, the amplification is less for a two-dimensional wedge than for a one-dimensional wedge. (iv) When the phase difference of ground motion at both ends of the dam equals π, the amplification for a two-dimensional wedge is less than that for a one-dimensional wedge, but when the phase difference equals nπ, (n > 1), the situation is reversed. (v) As the coefficient of truncation, h/H, increases, the displacement model partecipations decrease monotically. (vi) In general, the displacement caused by an earthquake is greater for a one-dimensional wedge than for a two-dimensional wedge when considering the seismic waves travelling, but the acceleration response of a two-dimensional wedge with long length of dam to travelling seismic waves with long dominant period is greater than that of a one-dimensional wedge. When the length of the dam is short enough, the response of a two-dimensional wedge without considering the influence of travelling seismic waves always gives the greatest value.     

Effect of seismic waves on the hydro-mechanical properties of fractured rock masses

The transmission of seismic waves in a particular region may influence the hydraulic properties of a rock mass, including permeability, which is one of the most important. To determine the effect of a seismic wave on the hydraulic behavior of a fractured rock mass, systematic numerical modeling was conducted. A number of discrete fracture network(DFN) models with a size of 20 m × 20 m were used as geometrical bases, and a discrete element method(DEM) was employed as a numerical simulation tool. Three different boundary conditions without(Type Ⅰ) and with static(Type Ⅱ) and dynamic(Type Ⅲ) loading were performed on the models, and then their permeability was calculated. The results showed that permeability in Type Ⅲ models was respectively 62.7% and 44.2% higher than in Type I and Type Ⅱ models. This study indicates that seismic waves can affect deep earth, and, according to the results, seismic waves increase the permeability and change the flow rate patterns in a fractured rock mass.     

Numerical models for the dynamic response of submerged floating tunnels under seismic loading

The modeling of tethering elements of seabed anchored floating structures is addressed, with particular reference to the so‐called Archimedes Bridge (submerged floating tunnel, SFT) solution for deep water crossing; attention is devoted to the design solution encompassing slender bars as anchor elements. Two numerical tools are proposed: firstly, a geometrically nonlinear finite element (NWB model), developed in previous work, has been refined in order to capture the effect of higher flexural modes of anchor bars. Secondly, a 3D beam element, based on the classical corotational formulation (CR model), has been developed and coded. Both elements are implemented in a numerical procedure for the dynamic time domain step‐by‐step analysis of nonlinear discretized systems; seismic loading is introduced by generating artificial time histories of spatially variable seismic motion. An example of application of the NWB element is shown regarding the behavior of the dynamic model of a complete SFT. The model was subjected to extreme multiple‐support seismic loading. The seismic behavior is here illustrated and commented, especially in light of the effect of higher local vibration modes of the anchor bars. Finally, a comparison between the performances of the two modeling approaches is presented. Both harmonic and seismic excitations are considered in the test; the results justify the use of the simpler NWB approach, especially in the SFT design phase. Copyright © 2008 John Wiley & Sons, Ltd.     

Research on propagation properties of elastic waves in two-phase anisotropic media

IntroductionItiswellknownthatanisotropylieswidelyintheundergroundmedia.Anisotropicmediawhicharemetintheseismicengineeringandseismicexplorationofenergyaremainlycausedbytheperiodicthinlayers(PTL)andextensivedilatancyanisotropy(EDA).Insuchmedia,anisotropyleadstomorecomplicatepropagationofseismicwave,thesignificantfeatureinanisotropicmediaisvelocityanisotropy.Infact,undergroundstrataareverycomplicated,whichareusuallycomposedofsolidframeandfluid(suchasoil,gasesorwater)inpores.Inordertostudyseism…     

An analysis method for elastic waves propagation in material involving cracks

In this paper, a new model to treat the problem of elastic wave travelling in rock mass that embeds cracks is proposed, in which, instead of modelling the crack directly the mechanical effects of discontinuities are translated into the equivalent nodal forces on a numerical procedure. Thus the response is physically obtained as the superposition of the incident wave field and the scattering wave field produced by the radiation of the reflected waves from the crack surfaces. Finally, a numerical example is carried out and it shows that the results by the proposed method have a very good agreement with those of the exact ones.     

Common-ray tracing and dynamic ray tracing for S waves in a smooth elastic anisotropic medium

Anisotropic common S-wave rays are traced using the averaged Hamiltonian of both S-wave polarizations. They represent very practical reference rays for calculating S waves by means of the coupling ray theory. They eliminate problems with anisotropic-ray-theory ray tracing through some S-wave slowness-surface singularities and also considerably simplify the numerical algorithm of the coupling ray theory for S waves. The equations required for anisotropic-common-ray tracing for S waves in a smooth elastic anisotropic medium, and for corresponding dynamic ray tracing in Cartesian or ray-centred coordinates, are presented. The equations, for the most part generally known, are summarized in a form which represents a complete algorithm suitable for coding and numerical applications.     

地震波诱发的深部地层动应力机制及断裂位移研究

借鉴弹性波动力学理论和爆破地震应力计算方法,结合地震波在岩层中的折射效应,以地震波加速度为基础数据,分析岩体在地震波作用下的受力。以汶川地震影响下的龙门山前陆盆地地下岩层的受力变形情况为例,通过计算分析和数值模拟,证实所用方法在求解分析地震波在各向同性岩石层间传播动力的可行性。同时验证汶川地震造成龙门山前陆盆地地下深部地层的断层破坏。      

Inelastic seismic response of torsionally unbalanced systems designed using elastic dynamic analysis

This paper evaluates the inelastic seismic response of torsionally unbalanced structural systems with strength distributed using elastic response spectrum analysis. The structural model is a single mass torsionally unbalanced system with lateral load resisting elements spanning in two principal directions. The element strength is distributed based on elastic response spectrum analysis and three different approaches to incorporate accidental torsion are considered: (a) without incorporating accidental torsion; (b) by applying static floor torques; (c) by shifting the location of the centre of mass. The seismic input is bidirectionally applied at the base of the model. It is shown that the inelastic responses depend strongly on the torsional stiffness of the system. For a torsionally stiff system, the torsional response leads to a decrease in the stiff edge displacement; however, for a torsionally flexible system, it tends to increase the stiff edge displacement. Using response spectrum analysis without including accidental torsion may lead to excessive additional ductility demand on the stiff edge element. With accidental torsion effect incorporated, the response spectrum analysis will give a strength distribution such that there will be no excessive additional ductility demands on the lateral load resisting elements.     

An improvement to linear‐elastic procedures for seismic performance assessment

An improved linear‐elastic analysis procedure is developed in this paper as a simple approximate method for displacement‐based seismic assessment of the existing buildings. The procedure is mainly based on reducing the stiffness of structural members that are expected to respond in the inelastic range in a single global iteration step. Modal spectral displacement demands are determined from the equal displacement rule. Response predictions obtained from the proposed procedure are evaluated comparatively by using the results of benchmark nonlinear response history analysis, and both the conventional and the multi‐mode pushover analyses. In comparative evaluations, a twelve‐story RC plane frame and a six‐story unsymmetrical‐plan RC frame are employed by using 91 ground motion components. It is observed that the proposed procedure estimates the flexural deformation demands in deformation‐controlled members and the shear forces in force‐controlled members with reasonable accuracy. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of travelling waves on stochastic seismic response and dynamic reliability of a long-span bridge on soft soil

It is generally known that the variability of earthquake ground motion is mainly in time and space. To investigate the impact of this variability on the seismic performance of a long-span flexible structure, we discuss the seismic dynamic responses of a real bridge subjected to stochastic seismic ground motion. We incorporate the effect of wave passage by means of the method of probability density evolution based on dynamic time-history analysis from the perspective of stochastic dynamics. First, we introduce the theory of probability density evolution and a category of stochastic seismic model. We then conduct a series of deterministic seismic dynamic analyses of the bridge to establish the probability density equation. Eventually, we obtain the probability information at the level of the probability density function of the seismic response by solving the probability-density evolution equation. The results show that the impact of travelling waves on a long-span structure is related to the characteristics of the earthquake ground motion and the structure, and that travelling waves increase the variability of the seismic response.     

Robust finite-difference scheme for elastic waves on coarse grids

Summary An explicit scheme for 2-D problems of P-SV waves is proposed, 4th order accurate in space and 2nd order accurate in time. The elastodynamic equations are discretized without destroying their self-adjoint nature. Twenty—four effective parameters are introduced at every grid point that make the scheme sensitive enough to spatial variations of the actual Lamé parameters. The scheme is of the same form everywhere, including discontinuities. In particular, also the free surface is described without special formulas; the so-called vacuum formalism is developed. These features make the method simple and widely applicable. However, boundary conditions are only approximately satisfied. Nevertheless, comparisons with independent methods indicate satisfactory results. They include, for example, local Rayleigh waves and bidimensional resonances in basin-like models with strongly curved interfaces of a high velocity contrast (1 : 5), whose principal features were modelled by the present method well.